Map Graphs
Discrete Mathematics
2007-05-23 v1 Data Structures and Algorithms
Abstract
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give an NP characterization for such graphs, and a cubic time recognition algorithm for a restricted version: given a graph, decide whether it is realized by adjacencies in a map without holes, in which at most four nations meet at any point.
Cite
@article{arxiv.cs/9910013,
title = {Map Graphs},
author = {Zhi-Zhong Chen and Michelangelo Grigni and Christos Papadimitriou},
journal= {arXiv preprint arXiv:cs/9910013},
year = {2007}
}
Comments
46 pages, LaTeX with 41 PS figures; see http://www.mathcs.emory.edu/~mic/mapgraphs/ for hi-res figures